Average Error: 0.0 → 0.0
Time: 1.8s
Precision: 64
\[\left(x + y\right) \cdot \left(x + y\right)\]
↓
\[x \cdot \left(x + y\right) + \left(y \cdot x + {y}^{2}\right)\]
\left(x + y\right) \cdot \left(x + y\right)
↓
x \cdot \left(x + y\right) + \left(y \cdot x + {y}^{2}\right)
double f(double x, double y) {
        double r888894 = x;
        double r888895 = y;
        double r888896 = r888894 + r888895;
        double r888897 = r888896 * r888896;
        return r888897;
}
↓
double f(double x, double y) {
        double r888898 = x;
        double r888899 = y;
        double r888900 = r888898 + r888899;
        double r888901 = r888898 * r888900;
        double r888902 = r888899 * r888898;
        double r888903 = 2.0;
        double r888904 = pow(r888899, r888903);
        double r888905 = r888902 + r888904;
        double r888906 = r888901 + r888905;
        return r888906;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.0
Target0.0
Herbie0.0
\[x \cdot x + \left(y \cdot y + 2 \cdot \left(y \cdot x\right)\right)\]

Derivation

  1. Initial program 0.0

    \[\left(x + y\right) \cdot \left(x + y\right)\]
  2. Using strategy rm

  3. Applied distribute-lft-in0.0

    \[\leadsto \color{blue}{\left(x + y\right) \cdot x + \left(x + y\right) \cdot y}\]

  4. Simplified0.0

    \[\leadsto \color{blue}{x \cdot \left(x + y\right)} + \left(x + y\right) \cdot y\]

  5. Simplified0.0

    \[\leadsto x \cdot \left(x + y\right) + \color{blue}{y \cdot \left(x + y\right)}\]
  6. Using strategy rm

  7. Applied distribute-lft-in0.0

    \[\leadsto x \cdot \left(x + y\right) + \color{blue}{\left(y \cdot x + y \cdot y\right)}\]

  8. Simplified0.0

    \[\leadsto x \cdot \left(x + y\right) + \left(y \cdot x + \color{blue}{{y}^{2}}\right)\]

  9. Final simplification0.0

    \[\leadsto x \cdot \left(x + y\right) + \left(y \cdot x + {y}^{2}\right)\]

Reproduce

herbie shell --seed 2020025 +o rules:numerics
(FPCore (x y)
  :name "Examples.Basics.BasicTests:f3 from sbv-4.4"
  :precision binary64

  :herbie-target
  (+ (* x x) (+ (* y y) (* 2 (* y x))))

  (* (+ x y) (+ x y)))